Applications of Fluid Mechanics on the Oroville Dam and Hyatt Power - - PowerPoint PPT Presentation

Applications of Fluid Mechanics on the Oroville Dam and Hyatt Power Plant

Rene Parra Tyler Booker Kristine Knecht Jessica Hanes David Carroll Chris Marinez

Oroville Dam

• East of the Sacramento Valley
• Built in 1963-1968
• Tallest dam in the US at 770 ft high
• Serves for water supply, flood

control and hydroelectricity generation

Hyatt Powerplant

• Building occurred through 1964-1967
• Underground, hydroelectric
• Pumps and Generators
• Focusing on the combined Pump

Generators

• Maximizes power by returning excess

water to the Lake Oroville

• Brought in through penstocks

Research Question 1:

How has the drought affected the hydrostatic force acting on the Oroville dam?

Hypothesis: By treating the dam as a flat trapezoid, an integral can be created in

• rder to calculate the different hydrostatic forces as the depth changes.

Hydrostatic Force

• By differentiating both

sides of the force equation, the following integral is formed

First step was to draw dam and get dimensions

• Crest length is 6920

ft

• Base height was

assumed to be 3460 ft by inspection

• Dam height is 770 ft

Next step was putting dA in terms of y

Finding BC in terms of y in order to find length AB with respect to y

AC=2BC+3460 AC=2(2.25y)+3460 ft dA=4.49y+3460 dy

Putting together the final integral

Final Force

Dam depth before and after drought Dam in December 2015 was 520 ft Dam in March 2016 was at 732 ft

Difference in Force before and after the Drought Before the drought the force was 3.58 x 1010 lbs After the drought the force was 7.62 x 1010 lbs This results in a 112% increase

Research Question 2:

Why is a trapezoidal shape a more logical and economical decision for a dam versus a rectangular shape?

Hypothesis: A trapezoidal dam shape makes more intuitive sense over a rectangular shape because it mirrors a standard hydrostatic pressure distribution

• curve. By application of the hydrostatic equation we find that the pressure force is

a function of depth. The dam is going to undergo a maximum force at the base of the dam according to this equation and decrease proportional to the thickness of the dam with a trapezoidal shape. A rectangular shape has a constant thickness which doesn’t work well with the changing magnitude of the hydrostatic force.

Hydrostatic Equation: Rectangular

Force from the Weight of the Structure: Rectangular

Resultant Force: Rectangular

Trapezoidal Details

Depth of Centroid

Hydrostatic Equation: Trapezoidal

Force from the Weight of the Structure: Trapezoidal

Resultant Force: Trapezoidal

Resultant Force: Rectangular vs Trapezoidal

Research Question 3:

Is it possible to lessen the head loss through the pumps in the Oroville Dam and Hyatt Powerplant? Hypothesis and approach:

• The power equation and Bernoulli’s Equation
• Givens are researched and found
• Adjustments are made for the best head loss
• Reasoning used to eliminate unrealistic solutions

The Power Equation

• 3 pumps, each with Q
• Density of water is 1.94 slugs/ft^3
• Gravity is 32.2 ft/s^2
• Power output is 97.4*10^6 ft*lb/s
• Flow Rate is 2,800 ft^3/s

Pump head = 556.9 ft

(per pump)

Bernoulli’s Equation

• With the pump head, Bernoulli’s

equation can be applied to find the head loss

• Assume position 1 is at the top of

the reservoir, exposed to air

• Position 2 is located at the

beginning of the river

Bernoulli’s Equation

Position 1:

• Pressure at surface = 0 psf
• Velocity at surface = 0 ft/s
• Height at surface = 770 ft
• Gravity = 32.2 ft/s^2

Position 2:

• Pressure at point 2 = ρgh = 374.8 psf
• Velocity at point 2 = Q/A = 7.37 ft/s
• Height at point 2 = -6 ft
• Density = 62.24 lb/ft^3
• Pump Head = 556.9 ft

Head Loss = 1,140 ft

Factors Affecting Head Loss

• Flow Rate: Higher velocity → higher head loss
• Pipe Diameter: Larger diameter → less friction → less head loss
• Roughness of Pipe Wall: Smoother surface → less friction → less head loss
• Length of the Pipe: Longer Pipe → more friction → more head loss
• Straightness of the Pipe: More bends → more friction → more head loss

Conclusions

• The depth of the dam varies by about 480 ft before and after the drought
• This results in a 112% increase in the Hydrostatic Force
• Trapezoidal shape is the better choice economically and structurally
• Not many realistic solutions to reduce head loss other than:
• decreasing flow rate
• changing depth of the water